Recently, [1]} demonstrated that Variational Autoencoders (VAEs) ([2]}) are able to find the best fitting financial model that can describe a large variety of volatility surfaces. They analyzed the FX market where they combined data from several currency pairs during the training process. They showed that a sufficiently trained VAE is not only able to interpolate between points on the volatility surface but in the case of sparse market data the decoder part of the VAE can efficiently reconstruct those missing points and provide a reliable extended surface. Although the results are very promising the trained neural network still remained a black box model which is relatively hard to interpret. Unlike the traditional approach, when we fit an analytic (e.g. SABR) model on the observed market and get the dynamics of the underlying asset, in case of VAEs we do not have any information about the stochastic processes under the hood. However, this information is crucial when we need to price more complex, path-dependent options (such as barriers). In our work we provide a hybrid solution for this problem where we combine the Deep Learning with a method called Weighted Monte Carlo method ([3]}).
